Let's fill in the blanks based on the context of multiplying decimals by 100 using expanded form.
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In the equation \( 345 x 100 \):
- We have: \( {(3x100) + (4x10) + (5x1)} x 100 = 30,000 + _ + 500 \)
- The blank should be filled with 40 (since \( 4 \times 10 = 40 \)).
- Now we summarize the equation: \( 30,000 + 40 + 500 = 30,540 \).
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The total after calculating would be:
- \( 30,000 + 40 + 500 = 30,540\).
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Compare to the original number:
- \( 34,500.00 \)
- \( 345.00 \)
- The digits 3, 4, and 5 each shifted two places to the left. This is because now their value is 100 times more than what it was before.
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Now analyzing \( 3.45 x 100 \):
- We have: \( {(3x1) + (4x0.1) + (5x0.01)} x 100 = 300 + _ + 5 \)
- The blank should be filled with 40 (since \( 4 \times 0.1 = 0.4 \) and when multiplied by 100 gives 40).
- Now summarizing: \( 300 + 40 + 5 = 345\).
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Compare to the original number:
- \( 345.00 \)
- \( 3.45 \)
- Again, each digit shifted two places to the left.
So the filled in paragraphs would be:
Multiplying Decimals by 100 Using Expanded Form
345 x 100
{(3x100) + (4x10) + (5x1)} x 100
30,000 + 40 + 500
30,540
Compare to the original number.
34,500.00
345.00
The digits 3, 4, and 5 each shifted two places to the left. This is because now their value is 100 times more than what it was before.
3.45 x 100
{(3x1) + (4x0.1) + (5x0.01)} x 100
300 + 40 + 5
345
Compare to the original number:
345.00
3.45
Again, each digit shifted two places to the left.
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